{"id":"https://openalex.org/W4391228326","doi":"https://doi.org/10.1080/10556788.2023.2285489","title":"Barzilai\u2013Borwein-like rules in proximal gradient schemes for \u2113 <sub>1</sub> -regularized problems","display_name":"Barzilai\u2013Borwein-like rules in proximal gradient schemes for \u2113 <sub>1</sub> -regularized problems","publication_year":2024,"publication_date":"2024-01-24","ids":{"openalex":"https://openalex.org/W4391228326","doi":"https://doi.org/10.1080/10556788.2023.2285489"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2023.2285489","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2023.2285489","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/11380/1330766","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070058552","display_name":"Serena Crisci","orcid":"https://orcid.org/0000-0001-9130-8163"},"institutions":[{"id":"https://openalex.org/I197809005","display_name":"University of Campania \"Luigi Vanvitelli\"","ror":"https://ror.org/02kqnpp86","country_code":"IT","type":"education","lineage":["https://openalex.org/I197809005"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Serena Crisci","raw_affiliation_strings":["Department of Mathematics and Physics, University of Campania \u2018L. Vanvitelli\u2019, Caserta, Italy","Department of Mathematics and Physics, University of Campania 'L. Vanvitelli', Caserta, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, University of Campania \u2018L. Vanvitelli\u2019, Caserta, Italy","institution_ids":["https://openalex.org/I197809005"]},{"raw_affiliation_string":"Department of Mathematics and Physics, University of Campania 'L. Vanvitelli', Caserta, Italy","institution_ids":["https://openalex.org/I197809005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006606154","display_name":"Simone Rebegoldi","orcid":"https://orcid.org/0000-0002-1232-5481"},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Simone Rebegoldi","raw_affiliation_strings":["Department of Industrial Engineering, University of Florence, Florence, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, University of Florence, Florence, Italy","institution_ids":["https://openalex.org/I45084792"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077915202","display_name":"Gerardo Toraldo","orcid":"https://orcid.org/0000-0001-9703-5557"},"institutions":[{"id":"https://openalex.org/I197809005","display_name":"University of Campania \"Luigi Vanvitelli\"","ror":"https://ror.org/02kqnpp86","country_code":"IT","type":"education","lineage":["https://openalex.org/I197809005"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gerardo Toraldo","raw_affiliation_strings":["Department of Mathematics and Physics, University of Campania \u2018L. Vanvitelli\u2019, Caserta, Italy","Department of Mathematics and Physics, University of Campania 'L. Vanvitelli', Caserta, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, University of Campania \u2018L. Vanvitelli\u2019, Caserta, Italy","institution_ids":["https://openalex.org/I197809005"]},{"raw_affiliation_string":"Department of Mathematics and Physics, University of Campania 'L. Vanvitelli', Caserta, Italy","institution_ids":["https://openalex.org/I197809005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075999000","display_name":"Marco Viola","orcid":"https://orcid.org/0000-0002-2140-8094"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Marco Viola","raw_affiliation_strings":["School of Mathematics and Statistics, University College Dublin, Dublin, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University College Dublin, Dublin, Ireland","institution_ids":["https://openalex.org/I100930933"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5070058552"],"corresponding_institution_ids":["https://openalex.org/I197809005"],"apc_list":null,"apc_paid":null,"fwci":1.3026,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7381713,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"39","issue":"3","first_page":"601","last_page":"633"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44324856996536255},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3903169631958008},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3548346757888794}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44324856996536255},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3903169631958008},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3548346757888794}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10556788.2023.2285489","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2023.2285489","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},{"id":"pmh:oai:iris.unimore.it:11380/1330766","is_oa":true,"landing_page_url":"https://hdl.handle.net/11380/1330766","pdf_url":null,"source":{"id":"https://openalex.org/S4306400718","display_name":"IRIS UNIMORE (University of Modena and Reggio Emilia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122346577","host_organization_name":"University of Modena and Reggio Emilia","host_organization_lineage":["https://openalex.org/I122346577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:iris.unimore.it:11380/1330766","is_oa":true,"landing_page_url":"https://hdl.handle.net/11380/1330766","pdf_url":null,"source":{"id":"https://openalex.org/S4306400718","display_name":"IRIS UNIMORE (University of Modena and Reggio Emilia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122346577","host_organization_name":"University of Modena and Reggio Emilia","host_organization_lineage":["https://openalex.org/I122346577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W1497361805","https://openalex.org/W1771758700","https://openalex.org/W1973307461","https://openalex.org/W1973734200","https://openalex.org/W2004461831","https://openalex.org/W2006262045","https://openalex.org/W2012341322","https://openalex.org/W2015131139","https://openalex.org/W2022611944","https://openalex.org/W2024829682","https://openalex.org/W2031127394","https://openalex.org/W2039050532","https://openalex.org/W2043430160","https://openalex.org/W2050892949","https://openalex.org/W2060581589","https://openalex.org/W2076605490","https://openalex.org/W2100556411","https://openalex.org/W2102790339","https://openalex.org/W2105630053","https://openalex.org/W2109062572","https://openalex.org/W2109449402","https://openalex.org/W2114605231","https://openalex.org/W2115706991","https://openalex.org/W2118075667","https://openalex.org/W2126607811","https://openalex.org/W2140163944","https://openalex.org/W2149454052","https://openalex.org/W2171413647","https://openalex.org/W2198227614","https://openalex.org/W2204799877","https://openalex.org/W2326893138","https://openalex.org/W2329996474","https://openalex.org/W2392724003","https://openalex.org/W2608443712","https://openalex.org/W2610492509","https://openalex.org/W2765202580","https://openalex.org/W2766258225","https://openalex.org/W2925918685","https://openalex.org/W2958002989","https://openalex.org/W2962721705","https://openalex.org/W2963433607","https://openalex.org/W2989871111","https://openalex.org/W3023463767","https://openalex.org/W3093906170","https://openalex.org/W3098069604","https://openalex.org/W3216569558","https://openalex.org/W4206006973","https://openalex.org/W4229706427","https://openalex.org/W4249513058","https://openalex.org/W4293094494","https://openalex.org/W4293775970","https://openalex.org/W4294564512"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"We":[0,48],"propose":[1],"a":[2,16,112,117,128,149,166],"novel":[3],"steplength":[4,56],"selection":[5],"rule":[6,26,110,139],"in":[7,38,68,160,165,172],"proximal":[8,113],"gradient":[9,42,114],"methods":[10,44],"for":[11,45,93,121],"minimizing":[12],"the":[13,30,39,50,54,58,69,72,75,81,84,89,97,108,134,137,142,145,162],"sum":[14],"of":[15,29,41,53,71,74,88,136,144,151],"differentiable":[17,59],"function":[18],"plus":[19],"an":[20],"\u21131-norm":[21],"penalty":[22],"term.":[23],"The":[24],"proposed":[25,138],"modifies":[27],"one":[28],"classical":[31],"Barzilai\u2013Borwein":[32],"steplength,":[33],"extending":[34],"analogous":[35],"results":[36],"obtained":[37],"context":[40],"projection":[43],"constrained":[46],"optimization.":[47],"analyse":[49],"spectral":[51],"properties":[52],"Barzilai\u2013Borwein-like":[55],"when":[57,96],"part":[60],"is":[61],"quadratic,":[62],"showing":[63],"that":[64,77],"its":[65,158],"reciprocal":[66],"lies":[67],"spectrum":[70,143],"submatrix":[73],"Hessian":[76,147],"depends":[78],"on":[79,148],"both":[80],"nonzero":[82],"and":[83],"nonoptimal":[85],"zero":[86,99],"components":[87,100],"current":[90],"iterate,":[91],"allowing":[92],"acceleration":[94],"effects":[95],"optimal":[98],"start":[101],"to":[102,140],"be":[103],"identified.":[104],"Furthermore,":[105],"we":[106,123],"insert":[107],"modified":[109],"into":[111],"method":[115],"with":[116],"nonmonotone":[118],"line":[119],"search,":[120],"which":[122],"prove":[124],"global":[125],"convergence":[126],"towards":[127],"stationary":[129],"point.":[130],"Numerical":[131],"experiments":[132],"show":[133],"ability":[135],"sweep":[141],"reduced":[146],"series":[150],"quadratic":[152],"\u21131-regularized":[153],"problems,":[154],"as":[155,157],"well":[156],"effectiveness":[159],"recovering":[161],"ground":[163],"truth":[164],"least":[167],"squares":[168],"regularized":[169],"problem":[170],"arising":[171],"image":[173],"restoration.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}
